## mmend98 one year ago The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the formula to an equivalent form that calculates three times a year, not just once a year. Which function is correct for Jackie's purpose, and what is the new growth rate? (5 points) f(x) = 4(4)x; growth rate 400% f(x) = 4(4)3x, growth rate 4% f(x) = 4(1.59)3x; growth rate 59% f(x) = 4(1.59)x; growth rate 4%

1. thomas5267

What is f(x) equal to? What is 4(4)x?

2. mmend98

I think it would be B.

3. mmend98

they are exponential as well the answers sorry for the typo

4. ganeshie8

rearrange the exponent as $$\frac{3x}{3}$$ and simplify : \large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\ &= 4(4^{\frac{1}{3}})^{3x}\\~\\ &= ? \end{align}}

5. mmend98

ok

6. ganeshie8

use ur calculator to work $$\large 4^{\frac{1}{3}}$$

7. mmend98

16.3

8. ganeshie8

nope, try again

9. ganeshie8

wolf says $$\approx 1.59$$ http://www.wolframalpha.com/input/?i=4%5E%281%2F3%29

10. mmend98

ah

11. mmend98

So the answer would be D?

12. mmend98

or C.

13. mmend98

14. ganeshie8

right, one of them how do we pin down which one it is

15. mmend98

it is c?

16. ganeshie8

how do you know

17. mmend98

because it is the same but manipulatd as the original equation

18. ganeshie8

rearrange the exponent as $$\frac{3x}{3}$$ and simplify : \large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\ &= 4(4^{\frac{1}{3}})^{3x}\\~\\ &= 4(1.\color{red}{59})^{3x}\\~\\ \end{align}} that red part gives you the growth rate

19. mmend98

oh ok.

20. ganeshie8

the fly population grows at a rate of $$59\%$$ per quarter

21. mmend98

we know c is the anser because 59 percent is the growht rate

22. mmend98

?

23. ganeshie8

yes ?

24. mmend98

yes

25. IrishBoy123

.